LEADER 02996nam 2200589 450 001 996466648303316 005 20220115221426.0 010 $a3-662-21569-1 024 7 $a10.1007/978-3-662-21569-2 035 $a(CKB)1000000000437442 035 $a(SSID)ssj0000322327 035 $a(PQKBManifestationID)11246288 035 $a(PQKBTitleCode)TC0000322327 035 $a(PQKBWorkID)10283213 035 $a(PQKB)11468650 035 $a(DE-He213)978-3-662-21569-2 035 $a(MiAaPQ)EBC5584854 035 $a(MiAaPQ)EBC6592311 035 $a(Au-PeEL)EBL5584854 035 $a(OCoLC)1066189399 035 $a(Au-PeEL)EBL6592311 035 $a(OCoLC)1250084100 035 $a(PPN)238020533 035 $a(EXLCZ)991000000000437442 100 $a20220115d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aConvex functions, monotone operators, and differentiability /$fRobert R. Phelps 205 $a1st ed. 1989. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1989] 210 4$dİ1989 215 $a1 online resource (XII, 120 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1364 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-50735-3 327 $aConvex functions on real Banach spaces -- Monotone operators, subdifferentials and Asplund spaces -- Lower semicontinuous convex functions -- A smooth variational principle and more about Asplund spaces -- Asplund spaces, the Radon-Nikodym property and optimization -- Gateaux differentiability spaces -- A generalization of monotone operators: Usco maps -- Notes and remarks. 330 $aThese notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1364 606 $aConvex functions 615 0$aConvex functions. 676 $a515.8 700 $aPhelps$b Robert R$g(Robert Ralph),$f1926-2013,$060176 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466648303316 996 $aConvex functions, monotone operators and differentiability$980225 997 $aUNISA